A robust regression approach to synthetic control with interference

TL;DR

This paper introduces a robust regression framework for synthetic control methods that accounts for interference among units, enabling valid inference in complex, real-world scenarios with unobserved confounding and unknown interference patterns.

Contribution

It develops a two-stage approach combining factor-model adjustment and robust regression to handle interference without prespecified controls or parametric interference models.

Findings

Robust regression achieves consistent control identification when many units are unaffected.

Method remains valid with sparse large and dense weak interference in diverging units.

Empirical applications reveal significant interference effects in policy impact studies.

Abstract

Synthetic control methods are widely used for policy evaluation, but most existing approaches rule out interference among units, compromising validity when such effects are present. We develop a framework that accommodates contaminated donor pools and unknown interference patterns through two stages: factor-model adjustment for unobserved confounding, followed by robust regression in which direct and interference effects appear as a sparse outlier component. We study two asymptotic regimes. When the number of units is fixed and at least half are unaffected by interference, high-breakdown robust regression yields consistent identification of valid controls and asymptotically normal inference. When the number of units diverges, we allow for sparse large and dense weak interference, with robust M-estimation remaining valid even when the post-intervention period is short. Unlike existing approaches requiring prespecification of valid controls or parametric modeling of interference, our framework relies only on coarse sparsity information and enables formal inference on both direct and interference effects. We assess the proposed methods through simulations and two empirical applications. An analysis of the US embassy relocation to Jerusalem reveals significant interference effects on conflict outcomes in Jordan, and an analysis of Beijing's air pollution policy uncovers spatial interference patterns consistent with prevailing wind directions.